Spurious Crests In Second-Order Waves
Occurrences of spurious crests on the troughs of large, relatively steep second-order Stokes waves are anomalous and not an inherent characteristic of real waves. Here, the effects of such occurrences on the statistics described by the standard second-order stochastic model are examined theoreticall...
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Large waves non-linear effects simulation spectra spurious crests Stokes waves wave breaking wave statistics. |
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Large waves non-linear effects simulation spectra spurious crests Stokes waves wave breaking wave statistics. M. A. Tayfun Spurious Crests In Second-Order Waves |
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Large waves non-linear effects simulation spectra spurious crests Stokes waves wave breaking wave statistics. |
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Occurrences of spurious crests on the troughs of large, relatively steep second-order Stokes waves are anomalous and not an inherent characteristic of real waves. Here, the effects of such occurrences on the statistics described by the standard second-order stochastic model are examined theoretically and by way of simulations. Theoretical results and simulations indicate that when spurious occurrences are sufficiently large, the standard model leads to physically unrealistic surface features and inaccuracies in the statistics of various surface features, in particular, the troughs and thus zero-crossing heights of large waves. Whereas inaccuracies can be fairly noticeable for long-crested waves in both deep and shallower depths, they tend to become relatively insignificant in directional waves. : {"references": ["R. G. Dean, and R. A. Dalrymple, Water Wave Mechanics for Engineers\nand Scientist., New Jersey: World Scientific, 1991, pp. 295-305.", "R. Miche, \"Mouvements ondulatoires de la mer en profoundeur onstante\nou decroissante. Annales des Ponts et Chaussees,\" vol. 121, pp. 285-318,\n1944.", "M. P. Tulin, and J. J. Li, \"On the breaking of energetic waves,\" Inter. J.\nOffshore Polar Eng.,vol. 2, pp. 46-53, 1992.", "M. A. Tayfun, \"Distributions of envelope and phase in wind waves,\" J.\nPhys. Oceanogr., vol. 38, pp. 2784-2800, 2008.", "Z. Cherneva, M. A. Tayfun , and C. Guedes Soares, 2009. \"Statistics of\nnonlinear waves generated in an offshore wave basin,\" J. Geophys. Res.,\nvol. 114, C08005, doi:10.1029/2009JC005332, 2009.", "A. Toffoli, A. Babanin, M. Onorato, and T. Waseda, \" Maximum\nsteepness of oceanic waves: field and laboratory experiments,\" Geophys.\nRes. Lett., vol. 37, L05603, doi:10.1029/2009GL041771, 2010.", "J. N. Sharma, and R. G. Dean, \"Development and evaluation of a\nprocedure for simulating a random directional second order sea surface\nand associated wave forces,\" Ocean Eng. Rep.20, University of\nDelaware, Newark. 1979.", "M. S. Longuet-Higgins, \"The effects of nonlinearities on statistical\ndistributions in the theory of sea waves,\" J. Fluid Mech. vol. 17, pp.\n459-480, 1963.", "L. Weber, and D. E. Barrick, \"On the nonlinear theory for gravity waves\non the ocean-s surface. Part I: derivations,\" J. Phys. Oceanogr., vol. 7,\npp. 3-10, 1977.\n[10] G. Z. Forristall, \"Wave crest distributions: observations and secondorder\ntheory,\" J. Phys. Oceanogr., vol. 30, pp. 1931-1943, 2000.\n[11] M. A. Tayfun, \"Distributions of envelope and phase in weakly nonlinear\nRandom waves,\" J. Eng. Mech., vol. 120, pp. 1009-1025, 1994.\n[12] M. A. Tayfun, \"Narrow-band nonlinear sea waves,\" J. Geophys. Res.,\nvol. 85, pp. 1548-1552, 1980.\n[13] M. A. Tayfun, and J-M. Lo, \"Envelope, phase, and narrowband models\nof sea waves,\" J. Waterw. Port, Coast. Ocean Eng., vol. 115, pp. 594-\n613, 1990.\n[14] F. Arena, and F. Fedele, \"A family of narrow-band nonlinear stochastic\nprocesses for the mechanics of sea waves,\" Eur. J. Mech. B/Fluids, vol.\n21, pp. 125-137, 2005.\n[15] M. A. Tayfun,\"Distribution of large wave heights,\" J. Waterway, Port,\nCoast. Ocean Eng., vol. 116, pp. 686-707, 1990.\n[16] P. Boccotti, \"On mechanics of irregular gravity waves,\" Atti Acc. Naz.\nLincei Memorie, vol. 19, pp. 111-170, 1989.\n[17] P. Boccotti, Wave mechanics for ocean engineering, Oxford: Elsevier\nScience, 2000, pp. 475-485.\n[18] F. Arena, \"On non-linear very large sea wave groups,\" Ocean Eng., vol.\n32, pp. 1311-1331, 2005.\n[19] F. Fedele, and F. Arena, \"Weakly nonlinear statistics of high random\nwaves,\" Phys. Fluids, vol. 17, pp. 026601:1-10, 2005.\n[20] F. Fedele, and M. A. Tayfun,\" On nonlinear wave groups and crest\nstatistics,\" J. Fluid Mech., vol. 620, pp. 221-239, 2009.\n[21] M. A. Tayfun, and F. Fedele, \"Wave-height distributions and nonlinear\neffects,\" Ocean Eng., vol. 34, pp. 1631-1649, 2007.\n[22] M. A. Tayfun,\"On the distribution of wave heights: nonlinear effects,\"\nin Marine Technology and Engineering, vol. 1, C. Guedes Soares, Y.\nGarbatov, N. Fonseca, and A. P. Teixeira, Eds. London: Taylor &\nFrancis Group, 2011, pp. 247-268.\n[23] G. Lindgren, \"Local maxima of Gaussian fields,\" Arkiv f\u252c\u00bf\u251c\u255dr Matematik,\nvol. 10, pp. 195-218, 1972.\n[24] O. M. Phillips, D. Gu, and M. Donelan, \"On the expected structure of\nextreme waves in a Gaussian sea. I. Theory and SWADE buoy\nmeasurements,\" J. Phys. Oceanogr., vol. 23, pp. 992-1000, 1993.\n[25] A. Toffoli, E. Bitner-Gregersen, M. Onorato, A. R. Osborne, and A. V.\nBabanin, \"Surface gravity waves from direct numerical simulations of\nthe Euler equations: A comparison with second-order theory,\" Ocean\nEng., vol. 35, pp. 367-379, 2008.\n[26] M. A. Tayfun, \"Statistics of nonlinear wave crests and groups,\" Ocean\nEng., vol. 33, pp.1589-1622, 2006.\n[27] M. A. Tayfun, \"A modified probability distribution for describing\nsecond-order sea waves,\" unpublished.\n[28] M. S. Longuet-Higgins, The statistical analysis of a random moving\nsurface. Philos. Trans. Roy. Soc. London, A966, pp. 321-387, 1957.\n[29] M. A. Tayfun, and F. Fedele, \"Expected shape of extreme waves in\nstorm seas,\" in Proc. 26th Inter. Conf. on Offshore Mech.& Arctic Eng.,\nSan Diego, paper no. OMAE2007-29073, pp. 1-8, 2007.\n[30] M. A. Donelan, J. Hamilton, and W. H. Hue, \"Directional spectra of\nwind-generated waves,\" Philos. Trans. Roy. Soc. London, A315, pp.\n509-562, 1985."]} |
format |
Text |
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M. A. Tayfun |
author_facet |
M. A. Tayfun |
author_sort |
M. A. Tayfun |
title |
Spurious Crests In Second-Order Waves |
title_short |
Spurious Crests In Second-Order Waves |
title_full |
Spurious Crests In Second-Order Waves |
title_fullStr |
Spurious Crests In Second-Order Waves |
title_full_unstemmed |
Spurious Crests In Second-Order Waves |
title_sort |
spurious crests in second-order waves |
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Zenodo |
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2013 |
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https://dx.doi.org/10.5281/zenodo.1082956 https://zenodo.org/record/1082956 |
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ENVELOPE(-84.767,-84.767,-78.617,-78.617) |
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https://dx.doi.org/10.5281/zenodo.1082957 |
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https://doi.org/10.5281/zenodo.1082956 https://doi.org/10.5281/zenodo.1082957 |
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ftdatacite:10.5281/zenodo.1082956 2023-05-15T15:20:30+02:00 Spurious Crests In Second-Order Waves M. A. Tayfun 2013 https://dx.doi.org/10.5281/zenodo.1082956 https://zenodo.org/record/1082956 en eng Zenodo https://dx.doi.org/10.5281/zenodo.1082957 Open Access Creative Commons Attribution 4.0 https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess CC-BY Large waves non-linear effects simulation spectra spurious crests Stokes waves wave breaking wave statistics. Text Journal article article-journal ScholarlyArticle 2013 ftdatacite https://doi.org/10.5281/zenodo.1082956 https://doi.org/10.5281/zenodo.1082957 2021-11-05T12:55:41Z Occurrences of spurious crests on the troughs of large, relatively steep second-order Stokes waves are anomalous and not an inherent characteristic of real waves. Here, the effects of such occurrences on the statistics described by the standard second-order stochastic model are examined theoretically and by way of simulations. Theoretical results and simulations indicate that when spurious occurrences are sufficiently large, the standard model leads to physically unrealistic surface features and inaccuracies in the statistics of various surface features, in particular, the troughs and thus zero-crossing heights of large waves. Whereas inaccuracies can be fairly noticeable for long-crested waves in both deep and shallower depths, they tend to become relatively insignificant in directional waves. : {"references": ["R. G. Dean, and R. A. Dalrymple, Water Wave Mechanics for Engineers\nand Scientist., New Jersey: World Scientific, 1991, pp. 295-305.", "R. Miche, \"Mouvements ondulatoires de la mer en profoundeur onstante\nou decroissante. Annales des Ponts et Chaussees,\" vol. 121, pp. 285-318,\n1944.", "M. P. Tulin, and J. J. Li, \"On the breaking of energetic waves,\" Inter. J.\nOffshore Polar Eng.,vol. 2, pp. 46-53, 1992.", "M. A. Tayfun, \"Distributions of envelope and phase in wind waves,\" J.\nPhys. Oceanogr., vol. 38, pp. 2784-2800, 2008.", "Z. Cherneva, M. A. Tayfun , and C. Guedes Soares, 2009. \"Statistics of\nnonlinear waves generated in an offshore wave basin,\" J. Geophys. Res.,\nvol. 114, C08005, doi:10.1029/2009JC005332, 2009.", "A. Toffoli, A. Babanin, M. Onorato, and T. Waseda, \" Maximum\nsteepness of oceanic waves: field and laboratory experiments,\" Geophys.\nRes. Lett., vol. 37, L05603, doi:10.1029/2009GL041771, 2010.", "J. N. Sharma, and R. G. Dean, \"Development and evaluation of a\nprocedure for simulating a random directional second order sea surface\nand associated wave forces,\" Ocean Eng. Rep.20, University of\nDelaware, Newark. 1979.", "M. S. Longuet-Higgins, \"The effects of nonlinearities on statistical\ndistributions in the theory of sea waves,\" J. Fluid Mech. vol. 17, pp.\n459-480, 1963.", "L. Weber, and D. E. Barrick, \"On the nonlinear theory for gravity waves\non the ocean-s surface. Part I: derivations,\" J. Phys. Oceanogr., vol. 7,\npp. 3-10, 1977.\n[10] G. Z. Forristall, \"Wave crest distributions: observations and secondorder\ntheory,\" J. Phys. Oceanogr., vol. 30, pp. 1931-1943, 2000.\n[11] M. A. Tayfun, \"Distributions of envelope and phase in weakly nonlinear\nRandom waves,\" J. Eng. Mech., vol. 120, pp. 1009-1025, 1994.\n[12] M. A. Tayfun, \"Narrow-band nonlinear sea waves,\" J. Geophys. Res.,\nvol. 85, pp. 1548-1552, 1980.\n[13] M. A. Tayfun, and J-M. Lo, \"Envelope, phase, and narrowband models\nof sea waves,\" J. Waterw. Port, Coast. Ocean Eng., vol. 115, pp. 594-\n613, 1990.\n[14] F. Arena, and F. Fedele, \"A family of narrow-band nonlinear stochastic\nprocesses for the mechanics of sea waves,\" Eur. J. Mech. B/Fluids, vol.\n21, pp. 125-137, 2005.\n[15] M. A. Tayfun,\"Distribution of large wave heights,\" J. Waterway, Port,\nCoast. Ocean Eng., vol. 116, pp. 686-707, 1990.\n[16] P. Boccotti, \"On mechanics of irregular gravity waves,\" Atti Acc. Naz.\nLincei Memorie, vol. 19, pp. 111-170, 1989.\n[17] P. Boccotti, Wave mechanics for ocean engineering, Oxford: Elsevier\nScience, 2000, pp. 475-485.\n[18] F. Arena, \"On non-linear very large sea wave groups,\" Ocean Eng., vol.\n32, pp. 1311-1331, 2005.\n[19] F. Fedele, and F. Arena, \"Weakly nonlinear statistics of high random\nwaves,\" Phys. Fluids, vol. 17, pp. 026601:1-10, 2005.\n[20] F. Fedele, and M. A. Tayfun,\" On nonlinear wave groups and crest\nstatistics,\" J. Fluid Mech., vol. 620, pp. 221-239, 2009.\n[21] M. A. Tayfun, and F. Fedele, \"Wave-height distributions and nonlinear\neffects,\" Ocean Eng., vol. 34, pp. 1631-1649, 2007.\n[22] M. A. Tayfun,\"On the distribution of wave heights: nonlinear effects,\"\nin Marine Technology and Engineering, vol. 1, C. Guedes Soares, Y.\nGarbatov, N. Fonseca, and A. P. Teixeira, Eds. London: Taylor &\nFrancis Group, 2011, pp. 247-268.\n[23] G. Lindgren, \"Local maxima of Gaussian fields,\" Arkiv f\u252c\u00bf\u251c\u255dr Matematik,\nvol. 10, pp. 195-218, 1972.\n[24] O. M. Phillips, D. Gu, and M. Donelan, \"On the expected structure of\nextreme waves in a Gaussian sea. I. Theory and SWADE buoy\nmeasurements,\" J. Phys. Oceanogr., vol. 23, pp. 992-1000, 1993.\n[25] A. Toffoli, E. Bitner-Gregersen, M. Onorato, A. R. Osborne, and A. V.\nBabanin, \"Surface gravity waves from direct numerical simulations of\nthe Euler equations: A comparison with second-order theory,\" Ocean\nEng., vol. 35, pp. 367-379, 2008.\n[26] M. A. Tayfun, \"Statistics of nonlinear wave crests and groups,\" Ocean\nEng., vol. 33, pp.1589-1622, 2006.\n[27] M. A. Tayfun, \"A modified probability distribution for describing\nsecond-order sea waves,\" unpublished.\n[28] M. S. Longuet-Higgins, The statistical analysis of a random moving\nsurface. Philos. Trans. Roy. Soc. London, A966, pp. 321-387, 1957.\n[29] M. A. Tayfun, and F. Fedele, \"Expected shape of extreme waves in\nstorm seas,\" in Proc. 26th Inter. Conf. on Offshore Mech.& Arctic Eng.,\nSan Diego, paper no. OMAE2007-29073, pp. 1-8, 2007.\n[30] M. A. Donelan, J. Hamilton, and W. H. Hue, \"Directional spectra of\nwind-generated waves,\" Philos. Trans. Roy. Soc. London, A315, pp.\n509-562, 1985."]} Text Arctic DataCite Metadata Store (German National Library of Science and Technology) Arctic Osborne ENVELOPE(-84.767,-84.767,-78.617,-78.617) |